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Many creative ideas are being proposed for image sensor designs, and these may be useful in applications ranging from consumer photography to computer vision. To understand and evaluate each new design, we must create a corresponding image…
Understanding the transformer architecture and its workings is essential for machine learning (ML) engineers. However, truly understanding the transformer architecture can be demanding, even if you have a solid background in machine…
Sequential data such as time series, video, or text can be challenging to analyse as the ordered structure gives rise to complex dependencies. At the heart of this is non-commutativity, in the sense that reordering the elements of a…
Animation elevates digital documents into immersive experiences, yet creating custom motion paths remains cumbersome, requiring designers to manually select presets, plot B\'ezier points, and configure timing properties. We introduce…
In this paper we consider a transformation $L_a$ of sequences of complex numbers. We find the inverse transformation of $L_a$ as well as the inverse of a related transformation $\tilde{L}_a$. We explore a connection to the binomial…
We provide a classification of the homogeneous 3-dimensional permutation structures, i.e. homogeneous structures in a language of 3 linear orders, partially answering a question of Cameron. We also arrive at a natural description of all…
Let $\mathcal{A}=(A_{1},...,A_{n},...)$ be a finite or infinite sequence of $2\times2$ matrices with entries in an integral domain. We show that, except for a very special case, $\mathcal{A}$ is (simultaneously) triangularizable if and only…
Machine learning (ML) offers powerful methods for detecting and modeling associations often in data with large feature spaces and complex associations. Many useful tools/packages (e.g. scikit-learn) have been developed to make the various…
We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a…
We describe several families of permutation polynomials obtained using functions with linear translators.
Usually, mathematical objects have highly parallel interpretations. In this paper, we consider them as sequential constructors of other objects. In particular, we prove that every reflexive directed graph can be interpreted as a program…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
It is known that any two triangulations of a compact 3-manifold are related by finite sequences of certain local transformations. We prove here an upper bound for the length of a shortest transformation sequence relating any two…
The symmetric group on a set acts transitively on its subsets of a given size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from…
Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the present work, we define and study a new subclass of tree-like…
e use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects…
We investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Restricting to the…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit…